A Distributionally Robust Optimization Model for Unit Commitment Considering Uncertain Wind Power Generation

Abstract

This paper proposes a distributionally robust optimization model for solving unit commitment (UC) problems considering volatile wind power generation. The uncertainty of wind power is captured by an ambiguity set that defines a family of wind power distributions, and the expected total cost under the worst-case distribution is minimized. Compared with stochastic programming, this method may have less dependence on the data of exact probability distributions. It should also outperform the conventional robust optimization methods because some distribution information can be incorporated into the ambiguity sets to generate less conservative results. In this paper, the UC model is formulated based on the typical two-stage framework, where the UC decisions are determined in a here-and-now manner, and the economic dispatch decisions are assumed to be wait-and-see , made after the observation of wind power outcomes. For computational tractability, the wait-and-see decisions are addressed by linear decision rule approximation, assuming that the economic dispatch decisions affinely depend on uncertain parameters as well as auxiliary random variables introduced to describe distributional characteristics of wind power generation. It is shown in case studies that this decision rule model tends to provide a tight approximation to the original two-stage problem, and the performance of UC solutions may be greatly improved by incorporating information on wind power distributions into the robust model.